相关论文: Harder-Narasimhan Filtrations and Zigzag Persisten…
Using sheaf theory, I introduce a continuous theory of persistence for mappings between compact manifolds. In the case both manifolds are orientable, the theory holds for integer coefficients. The sheaf introduced here is stable to…
We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schr\"odinger operator with a periodic potential plus a finitely supported perturbation. We describe all…
We study the representation theory of quantizations of Gieseker moduli spaces. Namely, we prove the localization theorems for these algebras, describe their finite dimensional representations and two-sided ideals as well as their categories…
In this paper we survey some finiteness results of the deformation classes of hyperk\"ahler Lagrangian fibrations, and we prove finiteness for stable Lagrangian fibrations with a given discriminant divisor.
We perform the so-called rigid lid limit on different shallow water models such as the abcd Bousssinesq systems or the Green-Naghdi equations. To do so we consider an appropriate nondimensionalization of these models where two small…
The aim of this paper is to extend the results of Giorgilli and Zehnder for aperiodic time dependent systems to a case of general nearly-integrable convex analytic Hamiltonians. The existence of a normal form and then a stability result are…
We introduce two new distances for zigzag persistence modules. The first uses Auslander-Reiten quiver theory, and the second is an extension of the classical interleaving distance. Both are defined over completely general orientations of…
A $d$-silting object is a silting object whose derived endomorphism algebra has global dimension $d$ or less. We give an equivalent condition, which can be stated in terms of dg quivers, for silting mutations to preserve the $d$-siltingness…
In this paper, we develop a stability threshold theorem for the 2D incompressible Navier-Stokes equations on the channel, supplemented with the no-slip boundary condition. The initial datum is close to the Couette flow in the following…
This paper studies a nonlinear fractional implicit differential equation (FIDE) with boundary conditions involving a HilferHadamard type fractional derivative. We establish the equivalence between the Cauchy-type problem (FIDE) and its…
Starting from our work on Harder-Narasimhan filtrations of finite flat group schemes over a $p$-adic field, we developp a theory of Harder-Narasimhan filtrations for $p$-divisible groups. We apply this to the study of the geometry of period…
A differential algebra of finite type over a field k is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated k-algebra. The prototypical example is the algebra of…
Three-dimensional direct numerical simulations of an incompressible open square cavity flow are conducted. Features of the permanent (non-linear) regime together with the linear stability analysis of a two-dimensional steady base flow are…
Results on stability of tautological sheaves on Hilbert schemes of points are extended to higher dimensions and transferred to abelian surfaces and to the restriction of tautological sheaves to generalised Kummer varieties. This provides a…
We consider an area-preserving diffeomorphism of a compact surface, which is assumed to be an irrational rotation near each boundary component. A finite set of periodic orbits of the diffeomorphism gives rise to a braid in the mapping…
We establish several foundational results regarding the Grothendieck-Springer affine fibration. More precisely, we prove some constructibility results on the affine Grothendieck-Springer sheaf and its coinvariants, enrich it with a group of…
The formation of patterns of peaks on the free surface of a ferrofluid subject to a magnetic field normal to the undisturbed interface is investigated theoretically. The relative stability of ridge, square, and hexagon planforms is studied…
A reduced divisor on a nonsingular variety defines the sheaf of logarithmic 1-forms. We introduce a certain coherent sheaf whose double dual coincides with this sheaf. It has some nice properties, for example, the residue exact sequence…
Ordinarily, quiver varieties are constructed as moduli spaces of quiver representations in the category of vector spaces. It is also natural to consider quiver representations in a richer category, namely that of vector bundles on some…
Inspired by Katz-Mazur theorem on crystalline cohomology and by Eskin-Kontsevich-Zorich's numerical experiments, we conjecture that the polygon of Lyapunov spectrum lies above (or on) the Harder-Narasimhan polygon of the Hodge bundle over…